= Unknown incidence offset in double-slit phase
For two narrow slits separated by $a$, oblique coherent illumination contributes a fixed relative incident <wave phase>. With a consistent angular convention, the observation-dependent <phase> is $\Delta\phi=(2\pi a/\lambda)(\sin\theta-\sin\alpha)$, where $\alpha$ is the unknown incidence angle.
The term containing $\alpha$ shifts the whole fringe sequence without changing the <phase> difference between two observed directions. Subtracting the conditions at adjacent bright and dark extrema eliminates this offset and leaves a <phase> change of $\pi$. This is the basis of <incidence-independent adjacent-fringe wavelength>; using the absolute position of one maximum without knowing $\alpha$ would confuse source tilt with <wavelength> or fringe order.
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